Serious obstacles hindering middle school students’ understanding of integer exponents

Abstract

This study aims to investigate the obstacles in eighth-grade students’ understanding of integer exponents using a mixed method research design. A total of 165 eighth-grade students were given a paper-pencil task and clinical interviews were conducted with 12 students. The findings indicated that achievement of the participants was low, especially in the zero and negative exponents. Students made errors that generally originated from the definition of exponentiation as repeated multiplication with natural numbers and underdeveloped conceptions of additive and multiplicative structures. As a result, the students overgeneralized the rules that are true for positive integer exponents to the other exponent expressions. Another crucial result was that most of the students did not know the meaning of zero exponents due to various obstacles due to the identity element of addition or the absorbing element of multiplication. Furthermore, students made various errors when undertaking operations with exponent expressions due to the confusion with additive and multiplicative structures in the operations of exponential expressions.